Metamath Proof Explorer

Theorem bi2anan9r

Description: Deduction joining two equivalences to form equivalence of conjunctions. (Contributed by NM, 19-Feb-1996)

	Ref	Expression
Hypotheses	bi2an9.1	$⊢ φ \to (ψ \leftrightarrow χ)$
	bi2an9.2	$⊢ θ \to (τ \leftrightarrow η)$
Assertion	bi2anan9r	$⊢ (θ \land φ) \to ((ψ \land τ) \leftrightarrow (χ \land η))$

Step	Hyp	Ref	Expression
1		bi2an9.1	$⊢ φ \to (ψ \leftrightarrow χ)$
2		bi2an9.2	$⊢ θ \to (τ \leftrightarrow η)$
3	1 2	bi2anan9	$⊢ (φ \land θ) \to ((ψ \land τ) \leftrightarrow (χ \land η))$
4	3	ancoms	$⊢ (θ \land φ) \to ((ψ \land τ) \leftrightarrow (χ \land η))$